Many mathematicians know that Lewis Carroll was quite a good mathematician, who wrote about logic (paradoxes) and determinants. He found an expansion formula, which bears his real name (Charles Lutwidge) Dodgson. Needless to say, L. Carroll was his pseudonym, used in literature.

Another (alive) mathematician writes under his real name and under a pseudonym (John B. Goode). (That person, by the way, is Bruno Poizat: it's no secret, even MathSciNet knows it.)

What other mathematicians (say dead ones) had a pseudonym, either within their mathematical activity, or in a parallel career ?

Of course, don't count people who changed name at some moment of their life because of marriage, persecution, conversion, and so on.

Edit.
The answers and comments suggest that there are at least four categories of pseudonyms, which don't exhaust all situations.

Professional mathematicians, who did something outside of mathematics under a pseudonym (F. Hausdorff - Paul Mongré, E. Temple Bell - John Taine),

One may type "pseudonym" into an "Anywhere" box at MathSciNet and find 44 hits. Many of these are not relevant to the question at hand, but I'll post any that I find that haven't been posted here already. Here's one: Christian Tapp, Kardinalitat und Kardinale, MR 2006h:01012, the review by Volker Peckhaus says that in Chapter 5, "We learn about [Georg] Cantor's pseudonyms such as Vincent Regnas, Jorge Vincente Monteador de Montemor, and others...."

Yet another find on MathSciNet. Anita Feferman, Politics, Logic, and Love, MR 93j:01010, reviewed by D J Struik. This is a biography of Jean van Heijenoort. "In 1948 he broke openly with his past in a paper of [sic] the Partisan Review, where he denied the scientific nature of Marxism. He wrote it under a pseudonym (Jean Vannier) - after all he was an alien and it was the McCarthy period."

Joseph Bernstein published a paper under the pseudonym "Yantarov" (which is derived from the Russian
translation of the German word "Bernstein" which means "amber").
At the time of writing he was an "otkaznik", a person waiting for permission to emigrate from the USSR,
and a paper under his own name would not be accepted.

Continuing to troll through MathSciNet, I find Yu I Krivonosov, Higher mathematics and higher authority, MR 2002k:01034, reviewed by R L Cooke (and I highly recommend the review). It seems that A I Lapin, a convicted anti-Soviet agitator, confined to an asylum in Leningrad, was allowed to publish under a pseudonym in 1952.

"De Leeuw is the originator[4] of the Albert Gifi team that wrote Nonlinear Multivariate Analysis.[5] In Multidimensional Scaling, Volume 1,[6] Cox and Cox write that "Albert Gifi is the nom de plume of members, past and present, of the Department of Data Theory at the University of Leiden who devised a system of nonlinear multivariate analysis that extends various techniques, such as principal components analysis and canonical correlation analysis." "

T. G. L. Zetters, has proven in 1979 that either player can draw in the 8-in-a-row game. This is a variant of the well known 5-in-a-row where players take turn placing their mark to a square on an infinite square grid, and a player wins if they have a consecutive sequence of 8 or more of his own marks in a row, column, or diagonal. According to the book Csákány Béla, Diszkrét Matematikai Játékok (Polygon, Szeged, 1998), this is a pseudonim of a group of Dutch mathematicians. According to the manuscript András Csernenszky, The Chooser-Picker 7-in-a-row-game (submitted in 2010, arXiv:1004.2460v1), it is a pseudonym for A. Brouwer.

Heinrich Seidel's review of M Lothaire, Combinatorics on Words, MR 84g:05002, says "The name of the author is a pseudonym chosen by the mathematicians who together with D Perrin serve as coauthors." There are about a dozen coauthors.

Hugo Steinhaus was also an author of aphorisms, which he published in the daily "Slowo Polskie" under a pseudonym Sestertius. Most were just goofy definitions of everyday terms. The following example seems to do OK in translation from Polish: "An opinion that all high-rank officers are stupid: a generalization". The book edition ("Slownik Racjonalny") appeared in 1980 (after his death) under his real name.

D'Alembert's name was in a sense a "pseudonym." D'Alembert was abandoned as an infant. However, d'Alembert was neither the name of his birth parents nor his adoptive parents. He made it up when he was a student.

Aristocles according to Wikipedia's article about him. I don't know if I knew that, but I've been familiar with the nickname meaning "broad-shouldered" or something like that for a long time.
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Michael HardyNov 8 '10 at 1:57

2

Who considers Plato a mathematician, and on what grounds?
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Gerry MyersonNov 8 '10 at 10:58

3

@Gerry: One person who considers Plato a mathematician put the assertion into the first paragraph of the Wikipedia article about him. It's in more than one place in the article and maybe more than one person put it there. You can look at the edit history, and maybe even find out the actual identities of those who did that. My uncertainty about the "grounds" you asked about was why I phrased my answer as a question.
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Michael HardyNov 8 '10 at 13:40

Here's one more from MathSciNet. N Ya Vilenkin, Formulas on cardboard, MR 93a:01039, reviewed by B Rosenfeld. Nikolay S Koshlyakov was arrested in 1942, was denounced as an "enemy of the nation," and was condemned to ten years in the camps. The book written by him in the camp, Investigations of a class of transcendental functions determined by the generalized equation of Riemann, was published ... in 1949 ... under the pseudonym N S Sergeev (Koshlyakov's patronymic name was Sergeevich).

According to Daniel Lazard, in his review of Berenstein and Struppa, Recent improvements in the complexity of the effective nullstellensatz, MR 92m:13024, N Fitchas was a pseudonym for a working group led by J Heintz that got results on the membership problem and the representation problem.

Another find on MathSciNet. Dominique Descotes, Genese des corollaires 1 et 2 de la lettre à Carcavy de Blaise Pascal, MR 99g:01016, review by Craig Fraser: In December of 1658 Blaise Pascal began to publish under the pseudonym A Dettonville the mathematical work Lettres de A Dettonville.... According to C B Boyer, "the name Amos Dettonville was an anagram of Louis de Montalte, the pseudonym used [by Pascal] in the Lettres provinciales."

Volume 1 of Statistical Methods of Model Building, edited by Helga Bunke and Olaf Bunke, was first published under the pseudonym of K M S Humak. See the review by J Kleffe, MR 88d:62121. See also MR 86b:62002.